I saw Maynard and his band in 1983 at the National Trumpet Symposium in Denver Colorado. Trust me, you don’t want to emulate anything that Maynard did. His chops looked like ground hamburger after performing and that’s the main thing I’ve always remembered about seeing him up close. Also, when Maynard talks about using a lot of air, he was clearly dealing with the Valsalva Manuever to force air past his firmly clamped together lips.
In 1983, Maynard was probably playing higher than just about every other trumpet player out there. But please, do yourself a favor and stick with Greg’s teaching. If you learn to play as high as he does with as little effort as Greg expends, you will be far better off than what Maynard was doing to his body.